Finite-Source Queueing Systems and their Applications
Finite-Source Queueing Systems and their Applications
Finite-Source Queueing Systems and their Applications
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János Sztrik 2001/08/05<br />
Queue length Q: The queue length, Q, is the number of jobs in the queue.<br />
Number of jobs in the system L: The number of jobs in the queueing<br />
system is represented by L. Then:<br />
L = E(L) =<br />
∞�<br />
kPk . (8)<br />
The mean number of jobs in the queueing system L, E(L) <strong>and</strong> the mean<br />
queue length Q, E(Q) can be calculated using one of the most important<br />
theorems of queueing theory, Little’s theorem, ( law ):<br />
k=1<br />
L = γT , Q = γW .<br />
Little’s theorem is valid for all queueing disciplines <strong>and</strong> arbitrary GI/G/m,<br />
<strong>and</strong> GI/G/K/N systems.<br />
<strong>Finite</strong>-<strong>Source</strong> <strong>Queueing</strong> <strong>Systems</strong> <strong>and</strong> <strong>their</strong> <strong>Applications</strong>
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